A notion of Poincaré series was introduced in [1]. It was developed in [2] for a multi-index filtration corresponding to the sequence of blow-ups. The present paper suggests the way to generalize the notion of Poincaré series to the case of arbitrary locally free sheaf on the modification of complex plane C 2. This series is expressed through the topological invariants of the sheaf. For the she...

A centrifugal route for separating small {110}-faceted gold nanostructures, namely rhombic dodecahedra (RD) and triangular bipyramids (BPs), which form simultaneously during synthesis and cannot be separated by means of conventional filtration methods, is presented. The centrifuged solution shows two distinct bands: i) RD and ii) BPs, as verified in the corresponding scanning electron microscop...

— We show that the limit, by rescaling, of the ‘new supersymmetric index’ attached to the Fourier-Laplace transform of a polarized variation of Hodge structure on a punctured affine line is equal to the spectral polynomial attached to the same object. We also extend the definition by Deligne of a Hodge filtration on the de Rham cohomology of a exponentially twisted polarized variation of comple...

— We show that the limit, by rescaling, of the ‘new supersymmetric index’ attached to the Fourier-Laplace transform of a polarized variation of Hodge structure on a punctured affine line is equal to the spectral polynomial attached to the same object. We also extend the definition by Deligne of a Hodge filtration on the de Rham cohomology of a exponentially twisted polarized variation of comple...

RESEARCH DESIGN AND METHODSdThis was a cohort study in adults with type 2 diabetes. Patients with known OSA or ESRD were excluded. DN was defined as the presence of albuminuria or an estimated glomerular filtration rate (eGFR) ,60 mL/min/1.73 m. DN progression was based on eGFR measurements. OSA was defined as apnea hypopnea index (AHI) $5 events/h. Serum nitrotyrosine abundance (a marker of ni...